TD: Algèbre générale: Lois, groupes, anneaux, corps

E={R→R}
F={R→[0; 1]}
T: (x;y)→xT y =x−yN R
(1 + i)R={z∈C∃x∈Rz= (1 + i)x}C
(1 + i)R C
nUn={z∈Czn= 1}
G=R+∗×R⊗R×R(x;y)⊗(a;b)=(xa;xb +y)
Z
ZnZ
∈N)
n∈NnZ={x∈Zx=np, p ∈Z}Z
ZnZ
HZ
H=ZH={0}
H6=ZH6={0}H∩N∗n0
H=n0Z
(G, ⊗)a, b ∈G2a⊗x=b
x⊗a=b
(E, o)E={R→R}o
foX =g X
(G, ⊗)e
G Z ={a∈G∀x∈G, a ⊗x=x⊗a}Z
G
∀x∈G, x ⊗x=e G

Z[i] = {a+ib, (a, b)∈Z2}Q[i] = {a+ib, (a, b)∈Q2}
Z[i]
Q[i]Z[i]
E={R→R}E
E
0
U
A f :x7→ x2A
K L ΦK L Φ